Lotus introduced a system they simply designated 'The Device' during Free Practice sessions in 2012 as a response to the FIA continuing to allow Mercedes the use of their DDRS (Double Drag Reduction System).
The mainstream media I believe have caused confusion amongst fans as they continue to call the Lotus style system DDRS when the systems are very different. The term DDRS should be used when the DRS mechanism is used for a secondary purpose just as Mercedes and Red Bull did in 2012 when stalling the Front Wing and Beam Wing on their cars respectively. This secondary function of DRS was utilised by these two teams by means of holes placed in the Rear Wing being exposed when DRS was deployed moving airflow to other regions of the car.
DRD however is a passive system and requires no interaction from another system or the driver to reduce drag at the rear of the car. As Lotus were the first team to utilise the device I will use theirs as my example.
DRD is made up of several additional components with different teams having tried different configurations along the way in order to both assess it's capabilities and fit within their own aero configuration. In the case of Lotus we have 5 main parts:
1. Airbox Ear's - Starting at the Front these little ducts move air down the internal tubing (2) toward the periscope.
3. Engine Cover Exhaust: Usually the engine cover stops much more abruptly at the rear of the car that when the 'device' is fitted. The additional exhaust section serves a few purposes: It allows the addition of the periscope that extends upto the rear wing but also acts as an exhaust for the airflow which exits into the beam wing Monkey Seat / Mini Diffuser.
4. Periscope: This is most important aspect of the whole system as it's how the air is transported to the underside of the Rear Wing in order to create the additional downforce at low speed and 'Stall' the rear wing over the speed threshold. In the picture below Lotus had the ejector holes taped over in order to stop the device operating (due to bad weather conditions)
5. Monkey Seat / Mini Diffuser is placed / being used in order to take advantage of the situation presented by the device in general. By adding this Diffuser shaped Monkey Seat the airflow will be pulled through the exhaust as Downforce is generated on top.
So now we understand the sum of the devices parts lets look at how it works and how much of a benefit it could offer. 
Air travels through the airbox ears out through the engine cover to the engine cover exhaust (depicted in blue), at a pre-determined speed threshold (measured by the team) the exit of the cover exhaust cannot extract the airflow it's being presented with. This allows the air to move up the Periscope and is ejected from the narrow slits placed on the sides of the periscope. The orientation of the slits means the airflow blows tangentially across the mainplane disrupting the regular airflow pattern sending the wing into a stall. (In order to adjust the speed threshold at which the device stalls the rear wing you must adjust the size of the outlet)
The problem the teams have faced whilst testing DRD is the ever changing conditions (climate) and car changes ie ride height etc. Furthermore this season will represent a different challenge for the devices as unlimited DRS usage is now unavailable for qualifying. This puts the onus on all the teams to use DRD and reduce the drag wherever possible but the time required to calibrate the device for it's passive switch eats into valuable setup time elsewhere on the cars setup.
The speed differential created by reducing drag via DRD will of course differ for the given application and as we have seen throughout 2012 and 2013's Testing different approaches have ensued. The other way to look at is how much downforce are you willing to give up? Teams with more downforce to trade off could start their stall earlier resulting in a higher top speed. So in summary although the innovation behind DRD is fantastic to see, it's adoption due it's passive nature remains to be seen. In terms of gains I'd speculate based on the gains seen by teams using the F Duct that a speed boost upwards of 5/8KMH could be seen on the straights.
DRD is perfectly legal as it requires no moving parts or interaction from the driver, it's activation is passive and relys on fluidic switching. The periscope lies within the central 15cm of the rear wing making it dimensionally legal and so unless the FIA deem the usage to be un-safe I don't see this being banned for 2013. In order to prohibit it's use the FIA would need to amend:
3.9.2 - No bodywork situated between 50mm forward of the rear wheel centre line and 150mm behind the rear wheel centre line, and which is between 75mm and 355mm from the car centre line, may be located between 400mm and 730mm above the reference plane.
Here's what we have seen in terms of DRD thus far:
Above: Lotus' application of blue flo-viz here helps us see the effects of DRD, the V formation on the mainplane indicates that the airflow in this region has separated causing the wing to stall allowing for a higher top speed.
Above: Mercedes version trialled from Spa onwards in 2012 featured a periscope that fell short of the underside of the rear wing. This would increase the distance at which the periscope could blow over the mainplane but would reduce it's targeting effect.
Above: Although this isn't DRD it seems Toro Rosso were evaluating running a centralised device when they tested at Abu Dhabi. Their appendage however featured two periscopes rather than one which could enable even more drag reduction.
Above: Last day of testing at Jerez (2013) and both Lotus and Mercedes placed their DRD's on the car to test but as we can see both have switched their design format effectively trying out each others designs.
As an aside we all know I don't have CFD in order to ascertain the credibility of my theories however as I have put forward in the past a way overcoming the switching effect required for DRD to work may be to introduce another flow construction enabling DRD's speed threshold to be lowered. To do this I'd look at the plausibilty of running DRD in conjunction with a mainplane hole like we have seen many teams utilise in the past. This may make tuning DRD easier as you now have another way of regulating the airflow in the central portion of the mainplane.
Lastly DRD has thus far been seen to be targeted at the Rear Wings Mainplane in order to reduce drag but just as Red Bull did from Singapore onwards with the use of DDRS I see no real reason why the Beam Wing couldn't be stalled through the use of DRD instead or aswell as. I look forward to seeing if/what teams decide to implement in regard to DRD throughout the 2013 season.
If you prefer to listen to what I'm explaining in this post then I have also compiled the information in the following video: